Feature Selection in NMF Models
The function featureScore implements different
methods to computes basis-specificity scores for each
feature in the data.
The function extractFeatures implements different
methods to select the most basis-specific features of
each basis component.
featureScore(object, ...)
## S4 method for signature 'matrix'
featureScore(object,
method = c("kim", "max"))
extractFeatures(object, ...)
## S4 method for signature 'matrix'
extractFeatures(object,
method = c("kim", "max"),
format = c("list", "combine", "subset"), nodups = TRUE)object |
an object from which scores/features are computed/extracted |
... |
extra arguments to allow extension |
method |
scoring or selection method. It specifies the name of one of the method described in sections Feature scores and Feature selection. Additionally for Note that |
format |
output format. The following values are accepted:
|
nodups |
logical that indicates if duplicated
indexes, i.e. features selected on multiple basis
components (which should in theory not happen), should be
only appear once in the result. Only used when
|
One of the properties of Nonnegative Matrix Factorization is that is tend to produce sparse representation of the observed data, leading to a natural application to bi-clustering, that characterises groups of samples by a small number of features.
In NMF models, samples are grouped according to the basis
components that contributes the most to each sample, i.e.
the basis components that have the greatest coefficient
in each column of the coefficient matrix (see
predict,NMF-method). Each group of samples
is then characterised by a set of features selected based
on basis-specifity scores that are computed on the basis
matrix.
featureScore returns a numeric vector of the
length the number of rows in object (i.e. one
score per feature).
extractFeatures returns the selected features as a
list of indexes, a single integer vector or an object of
the same class as object that only contains the
selected features.
signature(object =
"matrix"): Select features on a given matrix, that
contains the basis component in columns.
signature(object = "NMF"):
Select basis-specific features from an NMF model, by
applying the method extractFeatures,matrix to its
basis matrix.
signature(object = "matrix"):
Computes feature scores on a given matrix, that contains
the basis component in columns.
signature(object = "NMF"):
Computes feature scores on the basis matrix of an NMF
model.
The function featureScore can compute
basis-specificity scores using the following methods:
Method defined by Kim et al. (2007).
The score for feature i is defined as:
S_i = 1 + 1/log2(k) sum_q [ p(i,q) log2( p(i,q) ) ]
,
where p(i,q) is the probability that the i-th feature contributes to basis q:
p(i,q) = W(i,q) / (sum_r W(i,r))
The feature scores are real values within the range [0,1]. The higher the feature score the more basis-specific the corresponding feature.
Method defined by Carmona-Saez et al. (2006).
The feature scores are defined as the row maximums.
The function extractFeatures can select features
using the following methods:
uses Kim et al. (2007) scoring schema and feature selection method.
The features are first scored using the function
featureScore with method ‘kim’. Then only
the features that fulfil both following criteria are
retained:
score greater than \hat{μ} + 3 \hat{σ}, where \hat{μ} and \hat{σ} are the median and the median absolute deviation (MAD) of the scores respectively;
the maximum contribution to a basis component is greater than the median of all contributions (i.e. of all elements of W).
uses the selection method used in
the bioNMF software package and described in
Carmona-Saez et al. (2006).
For each basis component, the features are first sorted by decreasing contribution. Then, one selects only the first consecutive features whose highest contribution in the basis matrix is effectively on the considered basis.
Kim H and Park H (2007). "Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis." _Bioinformatics (Oxford, England)_, *23*(12), pp. 1495-502. ISSN 1460-2059, <URL: http://dx.doi.org/10.1093/bioinformatics/btm134>, <URL: http://www.ncbi.nlm.nih.gov/pubmed/17483501>.
Carmona-Saez P, Pascual-Marqui RD, Tirado F, Carazo JM and Pascual-Montano A (2006). "Biclustering of gene expression data by Non-smooth Non-negative Matrix Factorization." _BMC bioinformatics_, *7*, pp. 78. ISSN 1471-2105, <URL: http://dx.doi.org/10.1186/1471-2105-7-78>, <URL: http://www.ncbi.nlm.nih.gov/pubmed/16503973>.
# random NMF model x <- rnmf(3, 50,20) # probably no feature is selected extractFeatures(x) # extract top 5 for each basis extractFeatures(x, 5L) # extract features that have a relative basis contribution above a threshold extractFeatures(x, 0.5) # ambiguity? extractFeatures(x, 1) # means relative contribution above 100% extractFeatures(x, 1L) # means top contributing feature in each component
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